V型立体纸雕的几何理论与算法的研究

立体书是一种独特的纸张艺术形式,有着精细的几何结构.针对一类特殊的V型立体纸雕进行了系统性的研究,给出了V型立体纸雕可实现性的充分条件,使其可以只借助2张支撑面的力量进行打开和关闭,同时在这个过程中所有的面片都保持刚性并且相互不产生自交.基于这些充分条件,文中分别实现了一个计算机辅助交互V型纸雕设计工具,以及一个基于体方法的自动生成算法.

A Geometric Study of V-style Pop-ups: Theories and Algorithms

Pop-up books are a fascinating form of paper art with intriguing geometric properties.In this paper,we present a systematic study of a simple but common class of pop-ups consisting of patches falling into four parallel groups,which we call v-style pop-ups.We give sufficient conditions for a v-style paper structure to be pop-uppable.That is,it can be closed flat while maintaining the rigidity of the patches,the closing and opening do not need extra force besides holding two patches and are free of intersections,and the closed paper is contained within the page border.These conditions allow us to identify novel mechanisms for making pop-ups.Based on the theory and mechanisms,we developed an interactive tool for designing v-style pop-ups and an automated construction algorithm from a given geometry,both of which guaranteeing the pop-uppability of the results.